There are many known ways of making mathematical models of three-dimensional surfaces. There are many possible applications for these techniques; however, these techniques are too difficult and/or expensive for ordinary consumers to use them for making accurate three-dimensional models, and thus too difficult or expensive to be used in application such as selecting or fitting clothing.
Problems in Modeling the Shape of Objects Such as the Human Body:
Modeling the shape of an object, such as a part of a human body as may be done for the fitting of clothing, is a difficult problem. Many of the difficulties of the problem lie in the nature of the existing techniques for modeling the shape, in the nature of the human body, and in the nature of clothing, and include the following:                Human bodies are not standardized.        Determining an accurate model for the shape, such as for custom-sized and fitted clothing, requires extensive measurements.        Existing techniques are expensive, awkward, inaccurate, and inconvenient for consumers to perform.        Standard sizes of clothing are based on models that are not accurate for most wearers of the clothing.        
To illustrate the difficulties, an expert seamstress or tailor making or fitting a garment makes a number of measurements of parts of an individual's body. Effectively, the seamstress makes a model of the individual's body parts; the seamstress may also create a physical model in the form of an adjustable seamstress's dummy from the measurements by adjusting the dummy according to the measurements. The seamstress's dummy is a physical model that is adjusted to reflect a mathematical model determined by the measurements. Even so, the clothing must be altered to fit on the actual individual, because the model is not sufficiently accurate.
Current Techniques for Constructing Models of Parts of the Human Body:
Automated systems exist for producing measurements of parts of the human body.
A. Laser Body-Scanning
A number of specialized systems in the area of tailoring exist that take measurements of a human body or parts using laser body-scanning. In these systems, the individual to be measured goes to a special facility to pose for measurement. At the facility, a highly precise light source, such as a safe laser light, is used to project a number of illuminated traces across the body in a precisely-known set of paths. The locations where the light of the traces is reflected from the surface constitute a set of precisely-located reference points upon which measurements relevant to the surface can be based. Digital cameras or other optical viewing sensors which are calibrated and located at precisely-known positions detect the laser light reflected from the individual's body where the light strikes the individual's body, and determine the viewing location of the trace paths as the light illuminates the traces. Using a mathematical process such as triangulation, this location information, along with the precise positions of the light source and of the camera, is processed to calculate the actual path locations on the surface of the individual's body and to produce a mathematical model of the surface of the individual's body.
Exemplary systems of this kind include Intellifit (intellifit.com/fitting_process and TC2 (tc2.com/products/body_scanner.html) (References fetched from the World Wide Web on Jan. 10, 2009).
Disadvantages of these kinds of systems include the following:                The systems require special equipment that must be calibrated precisely.        The systems cannot be used in the consumer's home environment.        The systems are invasive: consumers need to wear minimum clothing in a semi-public setting.        The use of lasers in the technology may give users a perception of physical risk.        
B. Key-in Measurement Systems
There are systems in which an individual takes measurements manually and the measurements are submitted electronically to a system that computes a three-dimensional model from the measurement data. These systems fall into two classes: those used to fit custom-made haute couture clothing, and those for consumer use at home
The haute couture systems require the kinds of measurements made generally by expert seamstresses for custom clothes; they merely automate the process of making the model from the measurements.
With home systems, the consumer, perhaps with the assistance of a person of her or his choice, makes measurements of the individual's body. The measurements are made at home, using a set of instructions. The consumer then inputs the values of the measurements to an electronic form, such as a Web page form, and the values are submitted to a system that computes a three-dimensional model for the shape of the individual's body part from the measurement data. The model may then be used to obtain clothing made or fitted according to the three-dimensional model.
Exemplary systems of this kind include MyShape (myshape.com), and My Virtual Model (myvirtualmodel.com/en/index.php) (references fetched from the World Wide Web on Jan. 10, 2009).
Difficulties with such consumer systems include:                The individual measurements made by consumers are not sufficiently accurate.        Making the many measurements themselves is laborious for the consumer. It is further laborious to submit all the measurements manually by typing them into the electronic form.        The process for submitting data is subject to data-entry errors.        It is not possible to get either a sufficient number of measurements or many special measurements that may be required.        
C. Feature-Based Modeling:
Feature-based modeling has been used to produce models of surfaces. Feature-based modeling produces a three-dimensional model of a surface from a set of two-dimensional images of the surface. The feature-based modeling system extracts features from the images. A feature represents an element of the surface which appears in an image belonging to the set of images. The feature specifies the location in the image at which the element appears. If a particular element appears in more than one image, a feature can be extracted for each of the appearances. The feature-based modeling system can use the different locations of the features in the images belonging to the set of the images to make the three-dimensional model of the surface. The operation of determining that more than one feature represents a particular element of the surface which appears in the images of the set of images is called correlating the features. An example of a system using the techniques of feature-based modeling is a computer vision system. Two general references to computer vision systems are “Computer Vision: A Modern Approach”, by David A. Forsyth and Jean Ponce, Prentice Hall, 2002, and “Multiple View Geometry in Computer Vision., 2nd Edition”, by Richard Hartley and Andrew Zisserman, Cambridge University Press, 2004. Kinds of feature-based modeling include stereo vision, which requires cameras that are precisely-calibrated for viewing angles, rotation and location to construct three-dimensional models using correlated features, and structure-from-motion, which does not require calibrated cameras to construct three-dimensional models using correlated features.
Feature-based modeling has also been applied to making dynamic models of objects and to motion capture of human bodies. An exemplary reference is “Uncalibrated Motion Capture Exploiting Articulated Structure Constraints”, David Lebowitz and Stefan Carlsson, Eighth IEEE Conference on Computer Vision 2001, Vancouver, British Columbia.
Production of a model of a surface from a set of images of the surface being modeled involves the following steps in both stereovision and structure-from-motion:                Images: A number of two-dimensional images from a variety of viewing angles of the surface are obtained.        Feature extraction: Features are extracted in each of a number of the two-dimensional images.        Feature correlation: The same features are identified and matched in multiple two-dimensional images. Another term for feature correlation is feature matching.        Model computation: Using information about the positions of correlated features in the images, a three-dimensional model of the surface is computed.        
Additional steps may be employed, such as a step of processing the image or information of the image, to improve the quality of the features.
To date, a serious limitation on the use of stereo vision to make models of surfaces is the need for precise calibration of one or more cameras with regard to location and orientation relative to the surface being modeled and also with regard to the camera's focal length, if an accurate model is to be produced from the correlated features. One reference that discloses the mathematics of camera calibration for stereo vision is “A Versatile Camera Calibration Techniques for High-Accuracy 3D Machine Vision Metrology Using Off-the-shelf TV Cameras and Lenses”, IEEE Journal of Robotics and Automation, Vol. RA-3, NO. 4, August, 1987.
A serious limitation to date on the use of structure-from-motion to make models of surfaces is that enough elements of the surface being modeled must appear in the images being used to make the model to permit the extraction of enough correlatable features to provide a density of correlated features which is sufficient to produce a model having the accuracy required for the model's intended applications. The human body is an example here: the surface of the human body ordinarily does not have enough elements which appear in images of the human body to permit extraction of enough correlatable features to permit construction of models of the body which are accurate enough to be used in fitting clothing.